April 16, 2024

Thematic Program on Mathematics in Quantum Information
July-August, 2009

August 10-14, 2009
Mathematics in Experimental Quantum Information Processing Workshop
held at Institute for Quantum Computing, Waterloo

Organizing Committee:
David Cory (MIT)
Joseph Emerson (University of Waterloo)
David Kribs (University of Guelph)
Raymond Laflamme (University of Waterloo)
Kevin Resch (University of Waterloo)
Aephraim Steinberg (University of Toronto)

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This workshop has arisen from the need and desire of experimentalists working toward implementations of various quantum information processing tasks to interact with mathematicians on the one hand, and mathematicians working in quantum information or on its periphery to participate in attempts to implement quantum computation and communication technologies on the other. Thus, by its very nature this workshop is heavily interdisciplinary. It is hoped that this event, held at the Institute for Quantum Computing in Waterloo, will lead to collaborations between scientists that would not have had the opportunity to interact otherwise. Some potential interaction points are discussed below.

Experimental quantum information aims to develop physical systems that can exhibit the requisite quantum properties as well as methods for controlling and characterizing these systems. This is a very challenging task that involves significant mathematical and statistical issues. Quantum properties, such as entanglement and superposition, are notoriously fragile. To harness these properties, two seemingly contradictory constraints are required: the systems must be completely isolated from their environment to fight decoherence, yet amenable to precise and rapid control by outside forces. Despite these constraints, several physical systems are being intensively investigated and rapid progress has been achieved over the last several years.

For example, entanglement is a critical quantum resource in most quantum information applications. Experiments with trapped ions have demonstrated 6 and 8 ion entangled states, where the 6 ion states have been used for quantum-enhanced phase measurements. Optical experiments have demonstrated key entangled states, known as graph states, in up to 6 optical photons. Nuclear magnetic resonance (NMR) experiments have demonstrated the production of 12 qubit pseudo-pure states; and recently a pair of superconducting qubits has, for the first time, been entangled. Key quantum logic gates and even small quantum computing algorithms have been demonstrated in several of these systems.

Quantum cryptography is arguably the most advanced quantum technology. This particular technology is dominated by optical implementations since photons can be distributed over large distances with low decoherence. Driven by improvements in entangled-photon source and detector technologies, quantum key distribution has been demonstrated over 100km in both fibre and free-space quantum channels. Several important questions remain in the theory of quantum cryptography and will have important consequences for the technology. Quantum key distribution has been shown to be secure under, as of yet, unrealistic conditions. Can we develop a working experimental system and prove that it is unconditionally secure even with all of its real world imperfections? Quantum key distribution systems can only tolerate a certain amount of errors before their security is potentially compromised. However, there remains a gap between the error rate of known secure systems and systems which we know are not secure. Can we develop protocols to close this gap and yield systems which are able to tolerate higher error rates, or achieve higher bit rates?


Tentative Workshop Schedule

Monday August 10 Theme: Tomography
9:00-9:50 Registration and coffee
9:50-10:00 Opening remarks
10:00-10:50 Robin Blume-Kohout (Perimeter Institute)
Tomography: What is it good for?
10:50-11:10 Break
11:10-12:00 Aephraim Steinberg (University of Toronto)
Measuring quantum states in the presence of fundamental symmetries
12:00-2:00 Lunch
2:00-2:30 Peter Turner (University of Tokyo)
Comparison of maximum-likelihood and linear reconstruction schemes in quantum measurement tomography
2:30-3:00 Colm Ryan (Institute for Quantum Computing)
Randomized benchmarking in liquid-state NMR
3:00-3:30 Break
3:30-4:20 David Cory (MIT)
Efficient and Robust Decoupling
5:00-7:00 Dinner in tent at IQC
Tuesday August 11 Theme: Numerical Ranges
9:30-10:00 Coffee
10:00-10:50 John Holbrook (University of Guelph)
Introduction to numerical ranges
10:50-11:10 Break
11:10-11:40 Marcus Silva (Université de Sherbrooke)
Numeric ranges and minimal fidelity guarantees in the physical realization of unitaries
11:40-2:00 Lunch
2:00-2:30 Yiu Tung Poon (Iowa State University)
Generalized numerical ranges and quantum error correction
2:30-3:00 Raymond Sze (University of Connecticut)
The (p,k) matricial ranges and quantum error correction
3:00-3:30 Break
3:30-4:20 Cedric Beny (National University of Singapore)
Inverting a channel with near-optimal worst-case entanglement fidelity
5:00-7:00 Dinner in tent at IQC
Wednesday August 12
9:30-10:00 Coffee
10:00-10:50 Man-Duen Choi (University of Toronto)
Hard results in the soft mathematics in quantum information
10:50-11:10 Break
11:10-12:00 Chi-Kwong Li (College of William and Mary)
Completely positive linear maps, unitary orbits, and quantum operations
12:00-2:00 Lunch
2:00-2:50 Claudio Altafini
Feedback schemes for radiation damping suppression in NMR: a control-theoretical perspective
3:30-5:30 Poster session on UW campus
6:00-8:00 Banquet -- University Club
Thursday August 13
9:30-10:00 Coffee
10:00-10:50 Karol Zyczkowski (Jagiellonian University)
Product numerical range: a versatile tool in the theory of quantum information
10:50-11:10 Break
11:10-12:00 Thomas Schulte-Herbrüggen (Munich Technical University)
Matching Lie and Markov properties in open quantum systems
12:00-2:00 Lunch
2:00-2:50 Masoud Mohseni (MIT)
Environment-Assisted Quantum Processes
2:50-3:10 Break
3:10-4:00 Bei-Lok Hu (University of Maryland)
Entanglement Dynamics between Two Qubits in a Quantum Field: Birth, Death and Revivals
4:00-5:00 IQC lab tours
5:00-7:00 Dinner in tent at IQC
Friday August 14
9:30-2:00 Discussion time for people who are interested, no talks scheduled, coffee will be served in the morning and lunch will be served

Confirmed Participants as of August 11, 2009

Full Name University/Affiliation
Altafini, Claudio SISSA - Int. School for Advanced Studies
Belinschi, Serban University of Saskatchewan
Beny, Cedric National University of Singapore
Choi, Man-Duen University of Toronto
Cory, David Massachusetts Institute of Technology
Floricel, Remus University of Regina
Ghosh, Arpita Indian Statistical Institute
Guenda, Kenza University of Algiers
Holbrook, John University of Guelph
Hu, Bei Lok University of Maryland
Hu, Bei-lok University of Maryland
Johnston, Nathaniel University of Guelph
Kim, Peter University of Guelph
Koo, Ja-Yong Korea University
Kribs, David University of Guelph
Laflamme, Raymond University of Waterloo
Lehman, Lauri Macquarie University
Li, Chi-Kwong College of William and Mary
Lim, Jacques Bunrith IRMAR
Magesan, Easwar IQC
McNicholas, Paul University of Guelph
McNicholas, Sharon University of Guelph
Meyer, Angela University of Cambridge
Mohseni, Masoud Massachusetts Institute of Technology
Mudalige, Nishan University of Guelph
Pereira, Rajesh J. University of Guelph
Poon, Yiu Iowa State University
Resch, Kevin Institute for Quantum Computing
Schönfeldt, Johann-Heinrich Macquarie University
Schulte-Herbrueggen, Thomas TU-Munich
Silva, Marcus Université de Sherbrooke
Sze, Raymond Nung-Sing University of Connecticut
Turner, Peter University of Tokyo
Wei, Tzu-Chieh University of Waterloo
Zyczkowski, Karol Jagiellonian University


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